Fourier meets möbius: Fast subset convolution

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2007, Pages 67-74

  Björklund, Andreas ^a   Husfeldt, Thore ^a   Kaski, Petteri ^b   Koivisto, Mikko ^b  

^a LUND UNIVERSITY   (Sweden)

^b UNIVERSITY OF HELSINKI   (Finland)

Author keywords

Convolution; M bius transform; Steiner tree

Indexed keywords

ALGORITHMS; CONVOLUTION; FOURIER TRANSFORMS; INTEGER PROGRAMMING; PROBLEM SOLVING; TREES (MATHEMATICS);

STEINER TREE; SUBSET CONVOLUTION;

SET THEORY;

EID: 35449001611     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1250790.1250801     Document Type: Conference Paper

References (28)

1. M. Aigner, Combinatorial Theory, Springer, Berlin, 1979.
2. N. Alon, R. Yuster, U. Zwick, Color-coding, J. ACM 42 (1995) 844-856.
3. A. Björklund, T. Husfeldt, Inclusion-exclusion algorithms for counting set partitions, in: Proc. 47th IEEE Symposium on Foundations of Computer Science (Berkeley, Oct. 22-24, 2006), IEEE Computer Society, Los Alamitos, CA, 2006, pp. 575-582.
4. G.E. Blelloch, K. Dhamdhere, E. Halperin, R-. Ravi, R. Schwartz, S. Sridhar, Fixed parameter tractability of binary near-perfect phylogenetic tree reconstruction, in: M. Bugliesi, B. Preneel, V. Sassone, I. Wegener (Eds.), Automata, Languages and Programming, 33rd International Colloquium (Venice, July 10-14, 2006), Proceedings, Part I, Lecture Notes in Computer Science 4051, Springer, Berlin, 2006, pp. 667-678.
5. D. Coppersmith, S. Winograd, Matrix multiplication via arithmetic progressions, J. Symbolic Comput. 9 (1990) 251-280.
6. S.E. Dreyfus, R.A. Wagner, The Steiner problem in graphs, Networks 1 (1971/72) 195-207.
7. B. Fuchs, W. Kern, D. Molle, S. Richter, P. Rossmanith, X. Wang, Dynamic programming for minimum Steiner trees, Theory Comput. Syst., to appear.
8. B. Fuchs, W. Kern, X. Wang, Speeding up the Dreyfus-Wagner algorithm for minimum Steiner trees, Math. Meth Oper. Res., to appear.
9. M. Fürer, Faster integer multiplication, in: Proc. 39th ACM Symposium on Theory of Computing (San Diego, June 11-13, 2007), these proceedings.
10. Z. Galil, O. Margalit, All pairs shortest paths for graphs with small integer length edges, J. Comput. System Sci 54 (1997) 243-254.
11. J.L. Ganley, Computing optimal rectilinear Steiner trees: a survey and experimental evaluation, Discrete Appl. Math. 90 (1999) 161-171.
12. M. Garey, D. Johnson, Computers and Intractability - A Guide to the Theory of NP-Completeness, W.H. Freeman &: Co., San Francisco, CA, 1979.
13. J. Guo, R. Niedermeier, S. Wernicke, Parametrized complexity of vertex cover variants, in: F. Dehne, A. López-Ortiz, J.-R-. Sack (Eds.), Algorithms and Data Structures, 9th International Workshop (Waterloo, Canada, Aug. 15-17, 2005), Lecture Notes in Computer Science 3608, Springer, Berlin, 2005, pp. 36-48.
14. D.B. Johnson, Efficient algorithms for shortest paths in sparse networks, J. ACM 24 (1977) 1-13.
15. R. Kennes, Computational aspects of the Moebius transform of a graph, IEEE Transactions on Systems, Man, and Cybernetics 22 (1991) 201-223.
16. n) algorithm for graph coloring and other partitioning problems via inclusion exclusion, in: Proc. 47th IEEE Symposium on Foundations of Computer Science (Berkeley, Oct. 22-24, 2006), IEEE Computer Society, Los Alamitos, CA, 2006, pp. 583-590.
17. D.K. Maslen, D.N. Rockmore, Generalized FFTs - α survey of some recent results, in: L. Finkelstein, W.M. Kantor (Eds.), Groups and Computation, II, American Mathematical Society, Providence, RI, 1997, pp. 183-237.
18. D. Mölle, S. Richter, P. Rossmanith, A faster algorithm for the Steiner tree problem, in: B. Durand, W. Thomas (Eds.), 23rd Symposium on Theoretical Aspects of Computer Science (Marseille, Feb. 23-25, 2006), Lecture Notes in Computer Science 3884, Springer, Berlin, 2006, pp. 561-570.
19. T. Polzin, S.V. Daneshmand, On Steiner trees and minimum spanning trees in hypergraphs, Oper. Res. Lett. 31 (2003) 12-20.
20. G.-C. Rota, On the foundations of combinatorial theory. I. Theory of Möbius functions. Z. Wahrscheinlichkeitstheorie und verw. Gebiete 2 (1964) 340-368.
21. A. Schönhage, V. Strassen, Schnelle Multiplikation großer Zahlen, Computing 7 (1971) 281-292.
22. J. Scott, T. Ideker, R.M. Karp, R. Sharan, Efficient algorithms for detecting signaling pathways in protein interaction networks, J. Comput. Biol. 13 (2006) 133-144.
23. R. Seidel, On the all-pairs-shortest-path problem in unweighted undirected graphs, J. Comput. System Sci 51 (1995) 400-403.
24. A. Shoshan, U. Zwick, All pairs shortest paths in undirected graphs with integer weights, in: Proc. 40th Symposium on Foundations of Computer Science (New York, Oct. 17-19, 1999), IEEE Computer Society, Los Alamitos, CA, 1999, pp. 605-614.
25. R.P. Stanley, Enumerative Combinatorics, Vol. I, Cambridge University Press, Cambridge, 1997.
26. D.M. Warme, Spanning Trees in Hypergraphs with Applications to Steiner Trees, Ph.D. Thesis, University of Virginia, 1998.
27. F. Yates, The Design and Analysis of Factorial Experiments, Technical Communication No. 35, Commonwealth Bureau of Soil Science, Harpenden, UK, 1937.
28. 2.81 infinite-precision multiplications, Inform. Process. Lett. 4 (1976) 155-156.